Snow, bad weather and the poor condition of some cars appeared to have slowed the operation on Wednesday in east Aleppo, where only a small number of rebels are still waiting to leave under an agreement with the Syrian government.
"The evacuation is still ongoing, monitors are still on site. About 300 private vehicles left overnight and this morning," the UN official said.
A rebel contact inside Aleppo said that the "evacuation operation is continuing and has not ended".
Syrian President Bashar al-Assad had appeared close to taking back control of Aleppo on Wednesday, but UN and rebel officials denied that an operation to evacuate militants and civilians from the city had been completed.
About 30,000 people had been evacuated from Aleppo by Wednesday in a nearly week-long operation, according to the International Committee of the Red Cross (ICRC), which has led the convoy of buses and ambulances with the Syrian Arab Red Crescent.
In Geneva, ICRC spokeswoman Krista Armstrong told Reuters that the evacuation "will still take quite some time, possibly most of today (Thursday)".